Motion calculation device and motion calculation method

ABSTRACT

A motion calculation device includes an image-capturing unit configured to capture an image of a range including a plane and outputs the captured image, an extraction unit configured to extract a region of the plane from the image, a detection unit configured to detect feature points and motion vectors of the feature points from a plurality of images captured by the image-capturing unit at a predetermined time interval; and a calculation unit configured to calculate the motion of the host device based on both of an epipolar constraint relating to the feature points and a homography relating to the region.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit from U.S. Provisional application Ser.No. 61/295,448, filed Jan. 15, 2010, and claims priority on JapanesePatent Application No. 2010-135487, filed Jun. 14, 2010, the contents ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENT

1. Field of the Invention

The present invention relates to a motion calculation device and amotion calculation method which calculates the motion of the host devicebased on captured images.

2. Description of Related Art

JP-A-2006-350897 describes a motion measurement device which measuresthe motion of a mobile object including image-capturing means based onan epipolar constraint relating to images captured by theimage-capturing means.

JP-T-2003-515827 describes a system which predicts the motion(egomotion) of transfer means including a camera based on a homographyrelating to the images captured by the camera.

However, in the motion measurement device described in JP-A-2006-350897,there is a problem in that, when there are a small number of featurepoints corresponding to, for example, a stationary object in an imagecaptured by an image-capturing unit, it is very difficult to calculatethe motion of the host device based on the epipolar constraint relatingto the feature points.

In the system described in JP-T-2003-515827, there is a problem in that,in the image captured by the image-capturing unit, when there isinsufficient texture in a region of a plane, it is very difficult tocalculate the motion of the host device based on the homography relatingto the plane.

SUMMARY OF THE INVENTION

The invention has been finalized in consideration of the above-describedsituation, and an object of the invention is to provide a motioncalculation device and a motion calculation method capable of stablycalculating the motion of the host device.

The invention has been finalized in order to solve the above-describedproblems, and provides a motion calculation device. The motioncalculation device includes an image-capturing unit configured tocapture an image of a range including a plane and outputs the capturedimage, an extraction unit configured to extract a region of the planefrom the image, a detection unit configured to detect feature points andmotion vectors of the feature points from a plurality of images capturedby the image-capturing unit at a predetermined time interval, and acalculation unit configured to calculate the motion of the host devicebased on both of an epipolar constraint relating to the feature pointsand a homography relating to the region.

In the motion calculation device, the calculation unit may minimize acost function based on the epipolar constraint and the homography tocalculate the motion.

The invention provides a motion calculation method in a motioncalculation device which calculates the motion of the host device. Themotion calculation method includes causing an image-capturing unit tocapture an image of a range including a plane and to output the capturedimage, causing an extraction unit to extract a region of the plane fromthe image, causing a detection unit to detect feature points and motionvectors of the feature points from a plurality of images captured by theimage-capturing unit at a predetermined time interval, and causing acalculation unit to calculate the motion of the host device based onboth of an epipolar constraint to the feature points and a homograph),relating to the region.

According to the invention, the motion calculation device calculates themotion of the host device based on the epipolar constraint relating tothe feature points in the images and the homography relating to theregion of the plane. Therefore, the motion calculation device can stablycalculate the motion of the host device compared to a where the motionof the host device is calculated based on either the epipolar constraintor the homography.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing the configuration of a camera systemaccording to an embodiment of the invention.

FIG. 2 is a flowchart showing the operation procedure of the motioncalculation device according to the embodiment of the invention.

DETAILED DESCRIPTION OF INVENTION First Embodiment

A first embodiment of the invention will be described in detail withreference to the drawings, FIG. 1 is a block diagram showing theconfiguration of a camera system. A camera system is provided in amobile object. The mobile object is, for example, a vehicle. The camerasystem includes a motion calculation device 10, and a control device 20.

The motion calculation device 10 captures an image of a range includinga plane (for example, the ground) and calculates the motion(hereinafter, referred to as a “camera motion”) of the host device basedon the captured image. The motion calculation device 10 outputs thecalculated camera motion to the control device 20.

The motion calculation device 10 includes an image-capturing unit 11, atracking unit (detection unit) 12, an extraction unit 13, and acalculation unit 14. The image-capturing unit 11 includes alight-receiving element, and the light-receiving surface of thelight-receiving element has a plurality of pixels. An optical image isformed on the light-receiving surface by an optical system. Theimage-capturing unit 11 captures age of a range including a plane in apredetermined cycle and outputs the captured image to the tracking unit12 and the extraction unit 13. Hereinafter, an image I captured by theimage-capturing unit 11 at the time t is denoted by an image I_(t).Hereinafter, in the coordinate system with the principal point of theimage-capturing unit 11 as the origin, the coordinate system with theoptical axis direction as the Z axis is referred to as a “cameracoordinate system” The direction of light incident at the coordinate(x_(p),y_(p)) in the camera coordinate system is denoted by a directionvector p=[x,y,z]^(T) (the superscript T means transposition). The pixelvalue of a point p constituting the image I_(t) is denoted by I_(t)(p)using the direction vector p. The pixel value may be calculated throughinterpolation from the pixel values of peripheral pixels. It is assumedthat the image-capturing unit 11 is calibrated in advance.

The image I_(t) captured by the image-capturing unit 11 in apredetermined cycle is input to the tracking unit 12. The tracking unit12 detects feature points from the image I_(t) using a Harris operatoror the like. The tracking unit 12 also detects the motion vectors of thefeature points. Hereinafter, a set of feature points extracted by thetracking unit 12 is denoted by a set S_(t). The tracking unit 12 detectsa corresponding point q_(k) corresponding to the same position in anobserved scene (for example, a subject of the image I_(t) for a k-thfeature point p_(k) constituting a set S_(t-1) of feature points in animage I_(t-1) captured at the time t−1 using a Lucas-Kanade method orthe like. Hereinafter, a set of feature point correspondences(p_(k),q_(k)) (i.e., a set of pairs of feature point and correspondingpoint) is denoted by Ψ_(t).

The tracking unit 12 excludes, from Ψ_(t), a feature pointcorrespondence (p_(k),q_(k)) which does not follow the epipolarconstraint relating to the feature points of a static background (forexample, captured ground or building) using RANSAC (RANdom SAmpleConsensus) or the like. The tracking unit 12 outputs the set Ψ_(t) offeature point correspondences to the calculation unit 14. The trackingunit 12 performs the above-described processing for each image I_(t) totrack the feature points within the mage.

The set Ψ_(t) of feature point correspondences is input from thetracking unit 12 to the calculation unit 14. A region of a, plane(hereinafter, referred to as a “plane region”) in the image I_(t) isinput from the extraction unit 13 to the calculation unit 14. Here, itis assumed that the plane region is expressed by a set Π_(t)={B_(i)|i=1. . . m} of a plurality of blocks obtained by dividing the image I_(t).It is also assumed that the initial value of the set Π_(t) ispredefined. For example, when the motion calculation device 10 isprovided in a vehicle, the initial value of the plane region Π_(t) isdefined by the blocks {B_(i)|i=1 . . . m} of a high-incidence region(for example, the second half of the image) with the ground in the imageI_(t).

The calculation unit 14 stores the vector n=[n_(x),n_(y),n_(z)]⁷ of athree-dimensional parameter representing a plane n_(x)X+n_(y)Y+n_(z)Z=1on the X-Y-Z coordinate system with a predetermined position as theorigin. Here, the initial value n₀ of the vector n is predefined basedon the installation orientation of the motion calculation device 10 withrespect to the plane on which the mobile object is connected to theground. For example, the initial value n₀ is predefined based on theinstallation orientation of the motion calculation device 10 withrespect to the ground on which the vehicle is connected.

The calculation unit 14 calculates the camera motion and the orientationof the plane (hereinafter, referred to as a “plane orientation”) withrespect to the host device based on both of an epipolar constraintrelating to the feature points and a homography relating to the planeregion. Specifically, the calculation unit 14 minimizes a cost functionbased on both of a set Ψ_(t) of feature point correspondences and aplane region Π_(t) to calculate a parameter μ=[ω^(T),t^(T),n^(T)]representing the camera motion and the plane orientation. Here, the canera motion is constituted by a rotation parameterω^(T)=[ω_(x),ω_(y),ω_(z)] and a translation vectort^(T)=[t_(x),t_(y),t_(z)]. The plane orientation is expressed byn^(T)=[n_(x),n_(y),n_(y)].

The cost function is expressed by Expression (1).

$\begin{matrix}{{Q_{1}(\mu)} = {{\sum\limits_{{p \in B},\mspace{14mu} {B \in \Pi_{t}}}{\alpha_{p}\left\{ {{I_{t}\left( {w\left( {p;\mu} \right)} \right)} - {I_{t - 1}(p)}} \right\}^{2}}} + {\sum\limits_{{({p,q})} \in \Psi_{t}}{\beta_{p}\left\{ {{q^{T}\lbrack t\rbrack} \times {R(\omega)}p} \right\}^{2}}} + {\lambda \left( {{t^{T}t} - v^{2}} \right)}^{2}}} & (1)\end{matrix}$

In Expression (1), [t]_(x) is a cross product operator of a vector twhich is expressed by a 3×3 matrix. R(ω) is a rotation matrix which isdefined by the rotation parameter ω. A warp function W in the first afunction which represents homography transformation for the plane regionand is defined in accordance with the parameter μ representing thecamera motion and the plane orientation. The first term is called ahomography constraint term and represents an error in the homographytransformation from the plane region of the image I_(t-1) to the planeregion of the image I_(t).

Here, it is assumed that, with the motion of the motion calculationdevice 10, a feature point p in the plane region of the image I_(t-1)moves to a feature point q in the plane region of the image I_(t). Inthis case, the relationship shown in Expression (2) is establishedbetween the feature point p and the feature point q.

q˜(R(ω)−tn^(T))p  (2)

In Expression (2), the symbol “˜” represents that the vectors of bothsides are in parallel and the same except for the scale. The vector pand the vector n expressed by the camera coordinate system at the timet−1. Meanwhile, the vector q and the vector t expressed by the cameracoordinate system at the time t.

Here, H=R(ω)−tn^(T) which is a 3×3 matrix is taken into consideration.If the row vectors of the matrix H are denoted by h₁, h₂, and h₃, thewarp function W which represents the transformation from the featurepoint p=[x,y,1]⁷ to the corresponding point q=[x′,y′,1]^(T) is expressedby Expression (3),

$\begin{matrix}{q = {{w\left( {p;\mu} \right)} = {\frac{1}{h^{T}p}\left( {H\; p} \right)}}} & (3)\end{matrix}$

The second term in Expression (1) is called an epipolar constraint termand represents the epipolar constraint. When the feature point movesfrom the coordinate p to the coordinate q, Expression (4) is satisfiedby the epipolar constraint.

q ^(T) [t]×R(ω)p=0  (4)

In general, the left side does not become “0” due to errors of theparameters and observation errors of the vector p and the vector q. Forthis reason, it is considered that the left side in Expression (4) is analgebraic error on the epipolar constraint. Thus, the second term inExpression (1) represents the sum of square errors concerning theepipolar constraint.

The third term in Expression (1) is a regularization term in which themagnitude of the translation vector is v. Here, α_(p), β_(p), and λ inExpression (1) are weight coefficients. The third term in Expression (1)is added to Expression (1) so as to resolve the scale ambiguity of thetranslation vector t. For example, when the speed information of themobile object is not obtained, v=1 may be set. In this case, theestimated distance the motion calculation device 10 to the plane and theestimated distance from the motion calculation device 10 to each featurepoint have values proportional to the norm of the translation vector t.

The calculation unit 14 improves the estimation value of the parameter μusing variate δ so as to minimize the cost function. The calculationunit 14 minimizes value of the cost function by, for example, aGauss-Newton method.

If the inside of each square error in Expression (1) is primarilyapproximated to the variate δ of the parameter μ, Expression (5) isestablished. Here, r_(w), r_(e), and r_(v) are residual errors on theparameters μ of the respective terms in Expression (5). r_(w) isexpressed by Expression (6), r_(e) is expressed by Expression (7), andr, is expressed by Expression (8),

$\begin{matrix}{{Q\left( {\mu + \delta} \right)} = {{\sum\limits_{p \in {B_{1}\mspace{14mu} \ldots \mspace{14mu} B_{m}}}{\alpha_{p}\left\{ {r_{w} + {J_{w}^{T}\delta}} \right\}^{2}}} + {\sum\limits_{{({p,q})} \in \Psi_{t}}{\beta_{p}\left\{ {r_{e} + {J_{e}^{T}\delta}} \right\}^{2}}} + {\lambda \left( {r_{v} + {J_{v}^{T}\delta}} \right)}^{2}}} & (5)\end{matrix}$r _(w) =I _(t)(w(p;μ))−I _(t-1)(p)  (6)

r _(e) =q ^(T) [t]×R(ω)p  (7)

r _(v) =t ^(T) t−v ²  (8)

If a definition is made as expressed by Expression (9), Jacobian J_(w)at the feature point p is expressed by Expression (10) using the currentset parameter set value μ=[ω^(T),t^(T),n^(T)].

$\begin{matrix}{\begin{bmatrix}x_{h} \\y_{h} \\z_{h}\end{bmatrix} = {\left\{ {{R(\omega)} - {t\; n^{T}}} \right\} p}} & (9) \\{J_{w} = {\frac{1}{z_{h}}\begin{bmatrix}{{{- g_{x}}y\; x_{h}} - {g_{y}\left( {1 - {y\; y_{h}}} \right)}} \\{{g_{x}\left( {1 + {x\; x_{h}}} \right)} + {g_{y}\left( {x\; y_{h}} \right)}} \\{{{- g_{x}}y} - {g_{y}x}} \\{- {g_{x}\left( {n^{T}p} \right)}^{- 1}} \\{- {g_{y}\left( {n^{T}p} \right)}^{- 1}} \\{\left( {{g_{x}x_{h}} + {g_{y}y_{h}}} \right)\left( {n^{T}p} \right)^{- 1}} \\{{g_{x}{x\left( {{x_{h}t_{z}} - t_{x}} \right)}} + {g_{y}{x\left( {{y_{h}t_{z}} - t_{y}} \right)}}} \\{{g_{x}{y\left( {{x_{h}t_{z}} - t_{x}} \right)}} + {g_{y}{y\left( {{y_{h}t_{z}} - t_{y}} \right)}}} \\{{g_{x}\left( {{x_{h}t_{z}} - t_{x}} \right)} + {g_{y}\left( {{y_{h}t_{z}} - t_{y}} \right)}}\end{bmatrix}}} & (10)\end{matrix}$

J_(e) which appears in the differentiation of the second term inExpression (5) is expressed by Expression (11). Here, Expression (12) isestablished, J_(v) which appears in the differentiation of the thirdterm in Expression (5) is expressed by Expression (13).

$\begin{matrix}{J_{e} = \begin{bmatrix}{{{\hat{q}}_{3}y} - {\hat{q}}_{2}} \\{{\hat{q}}_{1} - {{\hat{q}}_{3}x}} \\{{{\hat{q}}_{2}x} - {{\hat{q}}_{1}y}} \\{{\hat{p}}_{2} - {{\hat{p}}_{3}y^{\prime}}} \\{{{\hat{p}}_{3}x^{\prime}} - {\hat{p}}_{1}} \\{{{\hat{p}}_{1}y^{\prime}} - {{\hat{p}}_{2}x^{\prime}}} \\0 \\0 \\0\end{bmatrix}} & (11) \\\left\{ \begin{matrix}{\begin{bmatrix}{\hat{p}}_{1} \\{\hat{p}}_{2} \\{\hat{p}}_{3}\end{bmatrix} = {{R(\omega)}p}} \\{\begin{bmatrix}{\hat{q}}_{1} \\{\hat{q}}_{2} \\{\hat{q}}_{3}\end{bmatrix} = {q^{T}\lbrack t\rbrack}_{x}}\end{matrix} \right. & (12) \\{J_{v} = {2{r_{v}\begin{bmatrix}0 \\0 \\0 \\{2t_{x}} \\{2t_{y}} \\{2t_{z}} \\0 \\0 \\0\end{bmatrix}}}} & (13)\end{matrix}$

If the differentiation for δ in Expression (5) is set to a value “0”,Expression (14) is established.

$\begin{matrix}{{{2{\sum\limits_{p}{\alpha_{p}J_{w}\left\{ {r_{w} + {J_{w}^{T}\delta}} \right\}}}} + {2{\sum\limits_{({p,q})}{\beta_{p}J_{e}\left\{ {r_{e} + {J_{e}^{T}\delta}} \right\}}}} + {2\lambda \; {J_{v}\left( {r_{v} + {J_{v}^{T}\delta}} \right)}}} = 0} & (14)\end{matrix}$

If a theorem is built for δ, Expression (14) is expressed by Expression(15).

$\begin{matrix}{{\left\lbrack {{\sum\limits_{p}{\alpha_{p}\left\{ {J_{w}J_{w}^{T}} \right\}}} + {\sum\limits_{({p,q})}{\beta_{p}\left\{ {J_{e}J_{e}^{T}} \right\}}} + {\lambda \; J_{v}J_{v}^{T}}} \right\rbrack \delta} = {{- {\sum\limits_{p}{\alpha_{p}\left\{ {r_{w}J_{w}} \right\}}}} - {\sum\limits_{({p,q})}{\beta_{p}\left\{ {r_{e}J_{e}} \right\}}} - {\lambda \; r_{v}J_{v}}}} & (15)\end{matrix}$

The left side in Expression (15) is the product of a 9×9 matrix and anine-dimensional parameter vector δ. The right side in Expression (15)is a nine-dimensional vector. As described above, Expression (15) is alinear simultaneous equation, such that a solution can be found for δ. δgives the approximate value (μ+δ) of the optimum value of the parameterestimation value μ.

As described above, the calculation unit 14 repeatedly updates theparameter estimation value μ until the value of the cost function ceasesto improve and, when the value of the cost function ceases to improve,determines that the solution converges. When the solution converges, thecalculation unit 14 outputs the parameter estimation valueμ=[(ω^(T),t^(T),n^(T)] to the extraction unit 13.

The weight coefficients α_(p), β_(p), and λ may be values experimentallydefined or may be defined as follows. Each term in Expression (1) is inthe form of square minimization, such that it can be seen that the costfunction expressed in Expression (1) is in the form of Expression (I)which represents a negative log likelihood based on the probabilitydistribution for each of the errors r_(w), r_(e), and r_(v).

$\begin{matrix}{{L(\mu)} = {{{- \log}{\prod\limits_{p}{p_{p}\left( {r_{w}\mu} \right)}}} - {\log {\prod\limits_{({p,q})}{p_{p,q}\left( {r_{e}\mu} \right)}}} - {\log \; {p\left( {r_{v}\mu} \right)}}}} & (I)\end{matrix}$

In Expression (I), the notation p(r|A) represents the probabilitydensity of the occurrence of the observed value r under the condition A.The subscript p of the first term in Expression (I) represents theprobability density function for each point p in the image. Thesubscripts p and q of the second term Expression (I) represent theprobability density function for each feature point correspondence(p,q).

If it is assumed that the probability distribution of each term is thenormal probability distribution, Expression (I) is expressed byExpression (II).

$\begin{matrix}{{L(\mu)} = {{c{\sum\limits_{p}\left\{ {\quad\frac{r_{w}^{2}}{2\sigma_{w}^{2}}}_{p} \right\}}} + {\sum\limits_{({p,q})}\left\{ {\quad\frac{r_{e}^{2}}{2\sigma_{e}^{2}}}_{({p,q})} \right\}} + \frac{r_{v}^{2}}{2\sigma_{v}^{2}}}} & ({II})\end{matrix}$

In Expression (II), the notation A|_((p,q)) represents the evaluation ofExpression A for the point p in the image. The notation A|_((p,q))represents the evaluation of Expression A for the feature pointcorrespondence (p,q) in the image, σ_(w) is the standard deviation oferror relating to the homography transformation. σ_(e) is the standarddeviation of error relating to the epipolar constraint. σ_(v) is thestandard deviation of error relating to the speed. The constant term Chas nothing to do with the minimization of Expression (II) and may thusbe negligible.

If Expression (II) is minimized, a parameter which maximizes thelikelihood of the observed value is estimated. Thus, when the noisestandard deviations σ_(w), σ_(e), and σ_(v) are given, α, β, and γ inExpression (1) are respectively the reciprocals of the squares of σ_(w),σ_(e), and σ_(v) from the viewpoint that the best likelihood value isestimated.

As described above, the weight coefficients α_(p), β_(p), and λ aredefined using the approximate model (Expression (II)) of therelationship between information concerning the luminance, gradient, andthe positions of the feature points in the image and the noise standarddeviations. In this way, it can be anticipated that the performance ofestimating the camera motion and the plane orientation is improvedcompared to a case where the weight coefficients are definedexperimentally.

Returning to FIG. 1, the description of the configuration will becontinued. The parameter estimation value μ calculated by thecalculation unit 14 is input to the extraction unit 13. The image I_(t)captured by the image-capturing unit 11 in a predetermined cycle isinput to the extraction unit 13. The extraction unit 13 divides theimage I_(t) into a plurality of blocks of a predefined size so as toextract a region of a plane from the image I. The extraction unit 13estimates the parameter (vector) n of the plane orientation for eachblack and extracts a set of blocks conforming to the plane orientationas a plane region.

In Expression (1), the first term which is the only term related to theplane orientation is used as the cost function on the plane orientation.The cost function on the plane orientation is expressed by Expression(16).

$\begin{matrix}{{Q_{B}(\mu)} = {\sum\limits_{p \in B}{\alpha_{p}\left\{ {{I_{t}\left( {w\left( {{p;n_{B}},\omega,t} \right)} \right)} - {I_{t - 1}(p)}} \right\}^{2}}}} & (16)\end{matrix}$

The value of the cost function of Expression (16) is minimized for theparameter n_(B) of the plane orientation of a block B. Here, as inExpression (1), the parameter n_(B) is updated by solving thesimultaneous equation (17) of the first term related to the planeorientation for each of both sites of Expression (15).

$\begin{matrix}{{\left\lbrack {\sum\limits_{p}\left\{ {J_{w}^{\prime}J_{w}^{\prime \; T}} \right\}} \right\rbrack \delta^{\prime}} = {- {\sum\limits_{p}\left\{ {\tau_{w}J_{w}^{\prime}} \right\}}}} & (17)\end{matrix}$

In Expression (17), J′_(w), is a vector which has only three componentsconcerning the parameter n of the plane orientation. δ′ is athree-dimensional vector for updating the three components related tothe parameter n of the plane orientation. That is, J′_(w) refers to thethree components in Expression (10) and is expressed by Expression (18).

$\begin{matrix}{J_{w}^{\prime} = {\frac{1}{z_{h}}\begin{bmatrix}{{g_{x}{x\left( {{x_{h}t_{z}} - t_{x}} \right)}} + {g_{y}{x\left( {{y_{h}t_{z}} - t_{y}} \right)}}} \\{{g_{x}{y\left( {{x_{h}t_{z}} - t_{x}} \right)}} + {g_{y}{y\left( {{y_{h}t_{z}} - t_{y}} \right)}}} \\{{g_{x}\left( {{x_{h}t_{z}} - t_{x}} \right)} + {g_{y}\left( {{y_{h}t_{z}} - t_{y}} \right)}}\end{bmatrix}}} & (18)\end{matrix}$

The left side in Expression (17) is the product of a 3×3 square matrixand a three-dimensional vector δ′. The right side in Expression (17) isa three-dimensional vector. Thus, δ′ is calculated as the solution ofthe linear simultaneous equation.

The extraction unit 13 calculates the difference between the parametern_(B) of the plane orientation of the block B and the parameter n of theplane orientation over the entire plane region. When the differencebetween the parameter n_(B) of the plane orientation and the parameter nof the plane orientation is equal to or smaller than a predeterminedthreshold value, the extraction unit 13 determines that the block 13 isa block which belongs to the plane region and adds the block B to theset Π_(t) of blocks to update the set Π_(t). Here, the predeterminedthreshold value is, for example, the Euclidean distance between theparameter n_(B) and the parameter n. The extraction unit 13 outputs theupdated set Π_(t) to the calculation unit 14.

The calculation unit 14 calculates nine parameters included in thecamera motion and the plane orientation based on the set Π_(t) updatedby the extraction unit 13. Here, with the stopping condition that thevalue of the cost function in Expression (1) is not improved, thecalculation unit 14 repeatedly calculates the nine parameters includedin the camera motion and the plane orientation until the stoppingcondition is satisfied. The calculation unit 14 outputs the finallycalculated camera motion and plane orientation to the control device 20.

Here, as the number of blocks representing the plane region decreases,the value of the cost function in Expression (1) decreases. As thenumber of blocks representing the plane region decreases, estimationaccuracy of the camera motion and the plane orientation is lowered.Thus, as the stopping condition for stopping the processing forcalculating the camera motion and the plane orientation, Expression (19)which is obtained by normalizing the first terra in Expression (1) withthe number of blocks may be used.

$\begin{matrix}{{Q^{\prime}(\mu)} = {{\frac{1}{\Pi_{t}}{\sum\limits_{{p \in B},\mspace{14mu} {B \in \Pi_{t}}}{\alpha_{p}\left\{ {{I_{t}\left( {w\left( {p;\mu} \right)} \right)} - {I_{t - 1}(p)}} \right\}^{2}}}} + {\sum\limits_{{({p,q})} \in \Psi_{t}}{\beta_{p}\left\{ {{q^{T}\lbrack t\rbrack} \times {R(\omega)}p} \right\}^{2}}} + {\lambda \left( {{t^{T}t} - v^{2}} \right)}^{2}}} & (19)\end{matrix}$

The camera and the plane orientation are input from the calculation unit14 of the motion calculation device 10 to the control device 20. Thecontrol device 20 performs predetermined processing based on the motionand the plane orientation. Here, the predetermined processing refers to,for example, processing in which the three-dimensional positions of thefeature points are calculated based on the camera motion throughtriangulation and, when a cluster of calculated feature points is acluster outside the plane region based on the plane orientation, thecluster is displayed on the shown) as an obstacle. For example, thepredetermined processing may be a processing in which an avoidancetraction is issued to the mobile object such that the mobile objectavoids the cluster outside the plane region. In this case, the issued toa vehicle including the camera system (motion calculation device 10 andcontrol device 20) such that the vehicle avoids another vehicle which istraveling ahead.

Next, the operation procedure of the motion calculation device 10 willbe described.

FIG. 2 is a flowchart showing the operation procedure of the motioncalculation device according to the embodiment of the invention.

The calculation unit 14 initializes the estimation value μ of the cameramotion and the plane orientation (Step S1). The image-capturing unit 11captures image of a range including a plane (Step S2). The tracking unit12 tracks the feature point p within the image. The tracking unit 12outputs the set Ψ_(t) of feature point correspondences to thecalculation unit 14 (Step S3). The calculation unit 14 calculates theestimation value μ of the camera motion and the plane orientation (StepS4).

The extraction unit 13 extracts the plane region (Step S5). Thecalculation unit 14 calculates the estimation value μ of the cameramotion and the plane orientation (Step S6). The calculation unit 14determines whether or not the solution converges (Step S7). When thesolution does not converge (Step S7—No), the operation of thecalculation unit 14 returns to Step S5. Meanwhile, when the solutionconverges (Step S7—Yes), the calculation unit 14 outputs the calculatedcamera motion and plane orientation to the control device 20. Thecontrol device 20 performs predetermined processing (scene analysis,display, warning, control, and the like) (Step S7).

As described above, the motion calculation device 10 includes theimage-capturing unit 11 which captures the image of the range includingthe plane and outputs the captured image, the extraction unit 13 whichextracts the region of the plane from the image, the tracking unit 12which detects the feature points and the motion vectors of the featurepoints from a plurality of images captured by the age-capturing unit IIat a predetermined time interval, and the calculation lit 14 whichcalculates the motion (camera motion) of the host device based on bothof the epipolar constraint relating to the feature points and thehomography relating to the region.

Thus, the motion calculation device can stably calculate the cameramotion compared to a case where the camera motion is calculated based oneither the epipolar constraint or the homography.

The calculation unit 14 minimizes the cost function based on theepipolar constraint and the homography to calculate the motion of thehost device. Thus, the motion calculation device can stably calculatethe camera motion based on the cost function.

Second Embodiment

A second embodiment of the invention will be described in detail withreference to the drawings. In the second embodiment, the regularizationterm of the cost function is different from that in the firstembodiment. Hereinafter, a description will be provided of onlydifferences from the first embodiment.

When it is assumed that the distance d between the principal point ofthe image-capturing unit 11 (see FIG. 1) and the plane is substantiallyconstant, the speed information (the magnitude of the translationvector) v of the host device may not be included in the regularizationterm (third term) in Expression (1). The relationship |n|²=d⁻² isestablished when the distance d between the principal point of theimage-capturing unit 11 and the plane expressed by n^(T)P=1 is expressedby d=−1/|n|. Thus, when it is assumed that the distance d between theprincipal point of the image-capturing unit 11 to the plane issubstantially constant, the cost function is expressed by Expression(20),

$\begin{matrix}{{Q_{d}(\mu)} = {{\sum\limits_{{p \in B},\mspace{14mu} {B \in \Pi_{t}}}{\alpha_{p}\left\{ {{I_{t}\left( {w\left( {p;\mu} \right)} \right)} - {I_{t - 1}(p)}} \right\}^{2}}} + {\sum\limits_{{({p,q})} \in \Psi_{t}}{\beta_{p}\left\{ {{q^{T}\lbrack t\rbrack} \times {R(\omega)}p} \right\}^{2}}} + {\lambda \left( {{n^{T}n} - d^{- 2}} \right)}^{2}}} & (20)\end{matrix}$

The calculation unit 14 minimizes the value of the cost function usingExpression (21), instead of Expression (8),

$\begin{matrix}{r_{v} = {{n^{T}n} - d^{- 2}}} & (21) \\{J_{v} = {2{r_{v}\begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\{2n_{x}} \\{2n_{y}} \\{2n_{z}}\end{bmatrix}}}} & (22)\end{matrix}$

The calculation unit 14 minimizes the value of the cost function usingExpression (22), instead of Expression (13).

As described above, the calculation unit 14 minimizes the cost function,which does not include the speed information v of the host device, tocalculate the motion of the host device. Thus, the motion calculationdevice can stably calculate the camera a without using the speedinformation v.

Although the embodiments of the invention have been described in detailwith reference to the drawings, the specific configuration is notlimited to the embodiments and may include design and the like withoutdeparting from the scope and spirit of the invention.

A program for implementing the above-described motion calculation devicemay be recorded in a computer-readable recording medium, and the programmay be loaded and executed on a computer system. The term “computersystem” used herein is a concept including an OS or hardware, such asperipheral devices. The “computer-readable recording medium” refers to aportable medium, such as a flexible disk, a magneto-optical disk, a ROM,or a CD-ROM, or a storage device, such as a hard disk incorporated intothe computer system. The “computer-readable recording medium” includes amedium which holds the program for a predetermined time such as avolatile memory (RAM) in the computer system which serves as a server ora client when the program is transmitted through a network, such asInternet, or a communication link, such as a telephone link. The programmay be transmitted from the computer system which stores the program inthe storage device or the like to another computer system through atransmission medium or transmission waves in the transmission medium.The “transmission medium” for transmitting the program refers to amedium having a function of transmitting information, for example, anetwork, such as Internet, or a communication link (communication line),such as a telephone link. The program may implement a portion of theabove-described function. The program may be a program which canimplement the above-described function through a combination with aprogram previously stored in the computer system, that is, a so-calleddifferential file (differential program).

While preferred embodiments of the invention have been described andillustrated above, it should be understood that these are exemplary ofthe invention and are not to be considered as limiting. Additions,omissions, substitutions, and other modifications can be made withoutdeparting from the spirit or scope of the present invention.Accordingly, the invention is not to be considered as being limited bythe foregoing description, and is only limited by the scope of theappended claims.

1. A motion calculation device comprising: an image-capturing unitconfigured to capture an image of a range including a plane and outputsthe captured image; an extraction unit configured to extract a region ofthe plane from the image; a detection unit configured to detect featurepoints and motion vectors of the feature points from a plurality ofimages captured by the image-capturing unit at a predetermined timeinterval; and a calculation unit configured to calculate the motion ofthe host device based on both of an epipolar constraint relating to thefeature points and a homography relating to the region.
 2. The motioncalculation device according to claim 1, wherein the calculation unit isconfigured to minimize a cost function based on the epipolar constraintand the homography to calculate the motion.
 3. A motion calculationmethod in a motion calculation device which calculates the motion of thehost device, the motion calculation method comprising: causing animage-capturing unit to capture an image of a range including a planeand to output the captured image; causing an extraction unit to extracta region of the plane from the image; causing a detection unit to detectfeature points and motion vectors of the feature points from a pluralityof images captured by the image-capturing unit at a predetermined timeinterval; and causing a calculation unit to calculate the motion of thehost device based on both of an epipolar constraint relating to thefeature points and a homography relating to the region.